Gammic temperament - Revision history

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	~~: This revision was by author~~ [[~~User:genewardsmith\|genewardsmith~~]] ~~and made on <tt>2010-07-09 00:15:06 UTC</tt>.<br>~~
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	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html"> </pre></div>
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	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gammic temperament</title></head><body></body></html></pre></div>

Wikispaces>genewardsmith: Imported revision 152023543 - Original comment:

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**Imported revision 152023543 - Original comment: **

← Older revision		Revision as of 00:15, 9 July 2010
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	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2010-07-09 00:04:24 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2010-07-09 00:15:06 UTC</tt>.<br>
	: The original revision id was <tt>~~152022947~~</tt>.<br>		: The original revision id was <tt>152023543</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
	<h4>Original Wikitext content:</h4>		<h4>Original Wikitext content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The [[Carlos Gamma]] rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20>. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = \|13 5 -9>, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, [[Schismatic family\|schismatic]] temperament makes for a natural comparison. Schismatic, with a wedgie of <<1 -8 -15\|\| is plainly much less complex than gammic with wedgie <<20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the [[34edo]] tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma if used for it.		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html"> </pre></div>

	Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of <<20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.

	~~===Neptune===~~
	A more interesting extension is to Neptune, which divides an octave plus a gammic generator in half, to get a 10/7 generator. Neptune adds 2401/2400 to the gammic comma, and may be described as the 68&171 temperament, with wedgie <<40 22 21 -58 -79 -13\|\|. The generator chain goes merrily on, stacking one 10/7 over another. until after eighteen generator steps 6/5 (up nine octaves) is reached. Then in succession we get 12/7, the neutral third, 7/4 and 5/4. Two neutral thirds then gives a fifth, and these intervals with their inverses are the full set of septimal consonances. [[171edo]] makes a good tuning, and we can also choose to make any of the consonances besides 7/5 and 10/7 just, including the fifth, which gives a tuning extending Carlos Gamma.

	Adding 385/384 or 1375/1372 to the list of commas allows for an extension to the 11-limit, where (7/5)^3 equates to 11/4. This may be described as <<40 22 21 -3 ...\|\| or 68&103, and 171 can still be used as a tuning, with val <171 271 397 480 591\|.

	~~An article on Neptune as an analog of miracle can be found [[http://tech.groups.yahoo.com/group/tuning-math/message/6001\|here]].~~
	</pre></div>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gammic temperament</title></head><body>The <a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a> rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20&gt;. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = \|13 5 -9&gt;, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, <a class="wiki_link" href="/Schismatic%20family">schismatic</a> temperament makes for a natural comparison. Schismatic, with a wedgie of &lt;&lt;1 -8 -15\|\| is plainly much less complex than gammic with wedgie &lt;&lt;20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the <a class="wiki_link" href="/34edo">34edo</a> tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma if used for it.<br />		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gammic temperament</title></head><body></body></html></pre></div>
	~~<br />~~
	Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of &lt;&lt;20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.<br />
	~~<br />~~
	~~<!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Neptune"></a><!-- ws:end:WikiTextHeadingRule:0 -->Neptune</h3>~~
	A more interesting extension is to Neptune, which divides an octave plus a gammic generator in half, to get a 10/7 generator. Neptune adds 2401/2400 to the gammic comma, and may be described as the 68&amp;171 temperament, with wedgie &lt;&lt;40 22 21 -58 -79 -13\|\|. The generator chain goes merrily on, stacking one 10/7 over another. until after eighteen generator steps 6/5 (up nine octaves) is reached. Then in succession we get 12/7, the neutral third, 7/4 and 5/4. Two neutral thirds then gives a fifth, and these intervals with their inverses are the full set of septimal consonances. <a class="wiki_link" href="/171edo">171edo</a> makes a good tuning, and we can also choose to make any of the consonances besides 7/5 and 10/7 just, including the fifth, which gives a tuning extending Carlos Gamma. <br />
	~~<br />~~
	Adding 385/384 or 1375/1372 to the list of commas allows for an extension to the 11-limit, where (7/5)^3 equates to 11/4. This may be described as &lt;&lt;40 22 21 -3 ...\|\| or 68&amp;103, and 171 can still be used as a tuning, with val &lt;171 271 397 480 591\|.<br />
	~~<br />~~
	~~An article on Neptune as an analog of miracle can be found <a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/6001" rel="nofollow">here</a>.~~</body></html></pre></div>

Wikispaces>genewardsmith: Imported revision 152022947 - Original comment:

2010-07-09T00:04:24Z

**Imported revision 152022947 - Original comment: **

← Older revision		Revision as of 00:04, 9 July 2010
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	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2010-07-~~01 18~~:58:50 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2010-07-09 00:04:24 UTC</tt>.<br>
	: The original revision id was <tt>~~151301605~~</tt>.<br>		: The original revision id was <tt>152022947</tt>.<br>
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	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The [[Carlos Gamma]] rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20>. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = \|13 5 -9>, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, [[Schismatic family\|schismatic]] temperament makes for a natural comparison. Schismatic, with a wedgie of <<1 -8 -15\|\| is plainly much less complex than gammic with wedgie <<20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the [[34edo]] tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma if used for it.		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The [[Carlos Gamma]] rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20>. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = \|13 5 -9>, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, [[Schismatic family\|schismatic]] temperament makes for a natural comparison. Schismatic, with a wedgie of <<1 -8 -15\|\| is plainly much less complex than gammic with wedgie <<20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the [[34edo]] tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma if used for it.

	Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of <<20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</pre></div>		Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of <<20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.

			===Neptune===
			A more interesting extension is to Neptune, which divides an octave plus a gammic generator in half, to get a 10/7 generator. Neptune adds 2401/2400 to the gammic comma, and may be described as the 68&171 temperament, with wedgie <<40 22 21 -58 -79 -13\|\|. The generator chain goes merrily on, stacking one 10/7 over another. until after eighteen generator steps 6/5 (up nine octaves) is reached. Then in succession we get 12/7, the neutral third, 7/4 and 5/4. Two neutral thirds then gives a fifth, and these intervals with their inverses are the full set of septimal consonances. [[171edo]] makes a good tuning, and we can also choose to make any of the consonances besides 7/5 and 10/7 just, including the fifth, which gives a tuning extending Carlos Gamma.

			Adding 385/384 or 1375/1372 to the list of commas allows for an extension to the 11-limit, where (7/5)^3 equates to 11/4. This may be described as <<40 22 21 -3 ...\|\| or 68&103, and 171 can still be used as a tuning, with val <171 271 397 480 591\|.

			An article on Neptune as an analog of miracle can be found [[http://tech.groups.yahoo.com/group/tuning-math/message/6001\|here]].
			</pre></div>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gammic temperament</title></head><body>The <a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a> rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20&gt;. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = \|13 5 -9&gt;, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, <a class="wiki_link" href="/Schismatic%20family">schismatic</a> temperament makes for a natural comparison. Schismatic, with a wedgie of &lt;&lt;1 -8 -15\|\| is plainly much less complex than gammic with wedgie &lt;&lt;20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the <a class="wiki_link" href="/34edo">34edo</a> tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma if used for it.<br />		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gammic temperament</title></head><body>The <a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a> rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20&gt;. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = \|13 5 -9&gt;, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, <a class="wiki_link" href="/Schismatic%20family">schismatic</a> temperament makes for a natural comparison. Schismatic, with a wedgie of &lt;&lt;1 -8 -15\|\| is plainly much less complex than gammic with wedgie &lt;&lt;20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the <a class="wiki_link" href="/34edo">34edo</a> tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma if used for it.<br />
	<br />		<br />
	Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of &lt;&lt;20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</body></html></pre></div>		Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of &lt;&lt;20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.<br />
			<br />
			<!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Neptune"></a><!-- ws:end:WikiTextHeadingRule:0 -->Neptune</h3>
			A more interesting extension is to Neptune, which divides an octave plus a gammic generator in half, to get a 10/7 generator. Neptune adds 2401/2400 to the gammic comma, and may be described as the 68&amp;171 temperament, with wedgie &lt;&lt;40 22 21 -58 -79 -13\|\|. The generator chain goes merrily on, stacking one 10/7 over another. until after eighteen generator steps 6/5 (up nine octaves) is reached. Then in succession we get 12/7, the neutral third, 7/4 and 5/4. Two neutral thirds then gives a fifth, and these intervals with their inverses are the full set of septimal consonances. <a class="wiki_link" href="/171edo">171edo</a> makes a good tuning, and we can also choose to make any of the consonances besides 7/5 and 10/7 just, including the fifth, which gives a tuning extending Carlos Gamma. <br />
			<br />
			Adding 385/384 or 1375/1372 to the list of commas allows for an extension to the 11-limit, where (7/5)^3 equates to 11/4. This may be described as &lt;&lt;40 22 21 -3 ...\|\| or 68&amp;103, and 171 can still be used as a tuning, with val &lt;171 271 397 480 591\|.<br />
			<br />
			An article on Neptune as an analog of miracle can be found <a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/6001" rel="nofollow">here</a>.</body></html></pre></div>

Wikispaces>genewardsmith: Imported revision 151301605 - Original comment:

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-06-22 18:06:53 UTC</tt>.<br>
: The original revision id was <tt>150072979</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two temperament tempering out |-29 -11 20>. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.
The generator in question is 1990656/1953125 = |13 5 -9>, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, [[Schismatic family|schismatic]] temperament makes for a natural comparison. Schismatic, with a wedgie of <<1 -8 -15|| is plainly much less complex than gammic with wedgie <<20 11 -29||, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the [[34edo]] tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma used for it.

Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of <<20 11 96 -29 96 192||. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gammic temperament</title></head><body>The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two temperament tempering out |-29 -11 20&gt;. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.<br />
The generator in question is 1990656/1953125 = |13 5 -9&gt;, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, <a class="wiki_link" href="/Schismatic%20family">schismatic</a> temperament makes for a natural comparison. Schismatic, with a wedgie of &lt;&lt;1 -8 -15|| is plainly much less complex than gammic with wedgie &lt;&lt;20 11 -29||, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the <a class="wiki_link" href="/34edo">34edo</a> tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma used for it.<br />
<br />
Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of &lt;&lt;20 11 96 -29 96 192||. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</body></html></pre></div>

← Older revision		Revision as of 18:58, 1 July 2010
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	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
	<h4>Original Wikitext content:</h4>		<h4>Original Wikitext content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20>. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = \|13 5 -9>, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, [[Schismatic family\|schismatic]] temperament makes for a natural comparison. Schismatic, with a wedgie of <<1 -8 -15\|\| is plainly much less complex than gammic with wedgie <<20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the [[34edo]] tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma if used for it.		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The [[Carlos Gamma]] rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20>. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = \|13 5 -9>, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, [[Schismatic family\|schismatic]] temperament makes for a natural comparison. Schismatic, with a wedgie of <<1 -8 -15\|\| is plainly much less complex than gammic with wedgie <<20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the [[34edo]] tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma if used for it.

	Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of <<20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</pre></div>		Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of <<20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</pre></div>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gammic temperament</title></head><body>The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20&gt;. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = \|13 5 -9&gt;, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, <a class="wiki_link" href="/Schismatic%20family">schismatic</a> temperament makes for a natural comparison. Schismatic, with a wedgie of &lt;&lt;1 -8 -15\|\| is plainly much less complex than gammic with wedgie &lt;&lt;20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the <a class="wiki_link" href="/34edo">34edo</a> tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma if used for it.<br />		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gammic temperament</title></head><body>The <a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a> rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20&gt;. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = \|13 5 -9&gt;, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, <a class="wiki_link" href="/Schismatic%20family">schismatic</a> temperament makes for a natural comparison. Schismatic, with a wedgie of &lt;&lt;1 -8 -15\|\| is plainly much less complex than gammic with wedgie &lt;&lt;20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the <a class="wiki_link" href="/34edo">34edo</a> tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma if used for it.<br />
	<br />		<br />
	Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of &lt;&lt;20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</body></html></pre></div>		Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of &lt;&lt;20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</body></html></pre></div>

← Older revision		Revision as of 18:57, 1 July 2010
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	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2010-06-22 18:09:16 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2010-07-01 18:57:37 UTC</tt>.<br>
	: The original revision id was <tt>~~150073231~~</tt>.<br>		: The original revision id was <tt>151301501</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
	<h4>Original Wikitext content:</h4>		<h4>Original Wikitext content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20>. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = \|13 5 -9>, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, [[Schismatic family\|schismatic]] temperament makes for a natural comparison. Schismatic, with a wedgie of <<1 -8 -15\|\| is plainly much less complex than gammic with wedgie <<20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the [[34edo]] tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma used for it.		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20>. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = \|13 5 -9>, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, [[Schismatic family\|schismatic]] temperament makes for a natural comparison. Schismatic, with a wedgie of <<1 -8 -15\|\| is plainly much less complex than gammic with wedgie <<20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the [[34edo]] tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma if used for it.

	Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of <<20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</pre></div>		Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of <<20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</pre></div>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gammic temperament</title></head><body>The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20&gt;. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = \|13 5 -9&gt;, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, <a class="wiki_link" href="/Schismatic%20family">schismatic</a> temperament makes for a natural comparison. Schismatic, with a wedgie of &lt;&lt;1 -8 -15\|\| is plainly much less complex than gammic with wedgie &lt;&lt;20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the <a class="wiki_link" href="/34edo">34edo</a> tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma used for it.<br />		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gammic temperament</title></head><body>The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20&gt;. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = \|13 5 -9&gt;, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, <a class="wiki_link" href="/Schismatic%20family">schismatic</a> temperament makes for a natural comparison. Schismatic, with a wedgie of &lt;&lt;1 -8 -15\|\| is plainly much less complex than gammic with wedgie &lt;&lt;20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the <a class="wiki_link" href="/34edo">34edo</a> tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma if used for it.<br />
	<br />		<br />
	Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of &lt;&lt;20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</body></html></pre></div>		Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of &lt;&lt;20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</body></html></pre></div>

← Older revision		Revision as of 18:09, 22 June 2010
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	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2010-06-22 18:08:44 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2010-06-22 18:09:16 UTC</tt>.<br>
	: The original revision id was <tt>~~150073169~~</tt>.<br>		: The original revision id was <tt>150073231</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
	<h4>Original Wikitext content:</h4>		<h4>Original Wikitext content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20>. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20>. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = \|13 5 -9>, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, [[Schismatic family\|schismatic]] temperament makes for a natural comparison. Schismatic, with a wedgie of <<1 -8 -15\|\| is plainly much less complex than gammic with wedgie <<20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the [[34edo]] tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma used for it.
	The generator in question is 1990656/1953125 = \|13 5 -9>, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, [[Schismatic family\|schismatic]] temperament makes for a natural comparison. Schismatic, with a wedgie of <<1 -8 -15\|\| is plainly much less complex than gammic with wedgie <<20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the [[34edo]] tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma used for it.

	Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of <<20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</pre></div>		Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of <<20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</pre></div>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gammic temperament</title></head><body>The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20&gt;. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.~~<br />~~		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gammic temperament</title></head><body>The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20&gt;. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.The generator in question is 1990656/1953125 = \|13 5 -9&gt;, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, <a class="wiki_link" href="/Schismatic%20family">schismatic</a> temperament makes for a natural comparison. Schismatic, with a wedgie of &lt;&lt;1 -8 -15\|\| is plainly much less complex than gammic with wedgie &lt;&lt;20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the <a class="wiki_link" href="/34edo">34edo</a> tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma used for it.<br />
	The generator in question is 1990656/1953125 = \|13 5 -9&gt;, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, <a class="wiki_link" href="/Schismatic%20family">schismatic</a> temperament makes for a natural comparison. Schismatic, with a wedgie of &lt;&lt;1 -8 -15\|\| is plainly much less complex than gammic with wedgie &lt;&lt;20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the <a class="wiki_link" href="/34edo">34edo</a> tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma used for it.<br />
	<br />		<br />
	Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of &lt;&lt;20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</body></html></pre></div>		Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of &lt;&lt;20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</body></html></pre></div>

← Older revision		Revision as of 18:08, 22 June 2010
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	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2010-06-22 18:06:53 UTC</tt>.<br>		: This revision was by author [[User:genewardsmith\|genewardsmith]] and made on <tt>2010-06-22 18:08:44 UTC</tt>.<br>
	: The original revision id was <tt>~~150072979~~</tt>.<br>		: The original revision id was <tt>150073169</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
	<h4>Original Wikitext content:</h4>		<h4>Original Wikitext content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two ~~temperament~~ tempering out \|-29 -11 20>. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20>. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.
	The generator in question is 1990656/1953125 = \|13 5 -9>, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, [[Schismatic family\|schismatic]] temperament makes for a natural comparison. Schismatic, with a wedgie of <<1 -8 -15\|\| is plainly much less complex than gammic with wedgie <<20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the [[34edo]] tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma used for it.		The generator in question is 1990656/1953125 = \|13 5 -9>, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, [[Schismatic family\|schismatic]] temperament makes for a natural comparison. Schismatic, with a wedgie of <<1 -8 -15\|\| is plainly much less complex than gammic with wedgie <<20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the [[34edo]] tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma used for it.

	Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of <<20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</pre></div>		Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of <<20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</pre></div>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gammic temperament</title></head><body>The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two ~~temperament~~ tempering out \|-29 -11 20&gt;. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.<br />		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Gammic temperament</title></head><body>The Carlos Gamma rank one temperament divides 3/2 into 20 equal parts, 11 of which give a 5/4. This is closely related to the rank two microtemperament tempering out \|-29 -11 20&gt;. This temperament, gammic, takes five generator steps to reach 5/4, and 20 to reach 3/2.<br />
	The generator in question is 1990656/1953125 = \|13 5 -9&gt;, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, <a class="wiki_link" href="/Schismatic%20family">schismatic</a> temperament makes for a natural comparison. Schismatic, with a wedgie of &lt;&lt;1 -8 -15\|\| is plainly much less complex than gammic with wedgie &lt;&lt;20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the <a class="wiki_link" href="/34edo">34edo</a> tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma used for it.<br />		The generator in question is 1990656/1953125 = \|13 5 -9&gt;, which when suitably tempered is very close to 5/171 octaves, which makes for an ideal gammic tuning. As a 5-limit temperament supported by 171-et, <a class="wiki_link" href="/Schismatic%20family">schismatic</a> temperament makes for a natural comparison. Schismatic, with a wedgie of &lt;&lt;1 -8 -15\|\| is plainly much less complex than gammic with wedgie &lt;&lt;20 11 -29\|\|, but people seeking the exotic might prefer gammic even so. The 34-note MOS is interesting, being a 1L33s refinement of the <a class="wiki_link" href="/34edo">34edo</a> tuning. Of course gammic can be tuned to 34, which makes the two equivalent, and would rather remove the point of Carlos Gamma used for it.<br />
	<br />		<br />
	Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of &lt;&lt;20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</body></html></pre></div>		Because 171 is such a strong 7-limit system, it is natural to extend gammic to the 7-limit. This we may do by adding 4375/4374 to the comma list, giving a wedgie of &lt;&lt;20 11 96 -29 96 192\|\|. 96 gammic generators finally reach 7, which is a long way to go compared to the 39 generator steps of pontiac. If someone wants to make the trip, a 103-note MOS is possible.</body></html></pre></div>

Gammic temperament - Revision history

Wikispaces>FREEZE at 00:00, 17 July 2018

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